<PRE><B>Question 1103757</B>
&lt;br&gt;
I will work the same problem but with different numbers, to show you the process.  Then you can practice using the process with your numbers.&lt;br&gt;
Here is my similar problem:&lt;br&gt;
You want to be able to withdraw $50,000 from your account each year for 25 years after you retire. If you expect to retire in 20 years and your account earns 5.5% interest while saving for retirement and 4.5% interest while retired....&quot;&lt;br&gt;&lt;br&gt;
a) How much will you need to have when you retire?&lt;br&gt;
This is a present value problem: you want to know how much you will need to have at the beginning (of retirement) to be able to withdraw $50,000 each year for 25 years.  The present value formula with an annual interest rate r and n periodic withdrawals each of amount A is
{{{x = A*((1-(1+r)^(-n))/r)}}}&lt;br&gt;
(NOTE: In this part of the problem, we are making withdrawals once a year, so the interest rate in the calculation is the annual interest rate.)&lt;br&gt;
With the numbers in my example, the formula is&lt;br&gt;
{{{x = 50000*((1-(1+.045)^(-25))/.045)}}}
{{{x = 50000*((1-.33273)/.045)}}}
{{{x = 50000*(.66727/.045)}}}
{{{x = 50000*14.8282}}}
{{{x = 741410.45}}}&lt;br&gt;
You will need $741,410.45 in the account when you retire in order to be able to withdraw $50,000 for 25 years.&lt;br&gt;
***NOTE***
I showed every step of the calculation; I of course used a calculator to perform the calculations.  I have seen students try to enter the entire formula into their calculators to get the answer; it is very easy to get parentheses in the wrong places.  Unfortunately, many students trust their calculators, so if they get an answer that says they need $47.6 million in their account in order to be able to withdraw $50,000 a year for 25 years, they believe it.&lt;br&gt;
The numbers at every stage should have some meaning; if your numbers are not similar, then you are not entering the calculations correctly on your calculator.&lt;br&gt;
The calculation (1+r)^-n should give a number between 0 and 1; so the next calculation 1 - (1+r)^-n should also give you a number between 0 and 1.&lt;br&gt;
The next number tells you the number of regular withdrawal amounts you should have in the account when you start making the withdrawals.  In my example, where I want to take withdrawals for 25 years, the number 14.8282 says the amount I have to have in the account at the beginning of those 25 years is only equal to the amount of less than 15 of those withdrawals -- so that is a good number to see.&lt;br&gt;
b) How much will you need to deposit each month until retirement to achieve your retirement goals?&lt;br&gt;
This is a future value problem: You want to know how much you need to deposit each month for the next 20 years to have the required amount $741,410.45 at the end of those 20 years.&lt;br&gt;
The future value formula for the amount of the regular monthly contribution necessary to accumulate an amount P, in n months with an annual interest rate r, is&lt;br&gt;
{{{P = x(((1+r/12)^n-1)/(r/12))}}}&lt;br&gt;
(NOTE: In this part of the problem, we are making deposits once a month, so the interest rate in the calculation is the monthly interest rate, which is 1/12 of the annual interest rate.)&lt;br&gt;
With the numbers in my example,
{{{741410.45 = x(((1+.055/12)^240-1)/(.055/12))}}}
{{{741410.45 = x((2.9966-1)/(.055/12))}}}
{{{741410.45 = x((1.9966)/(.055/12))}}}
{{{741410.45 = x(435.63)}}}
{{{x = 741710.45/435.63 = 1701.94}}}&lt;br&gt;
The amount of the monthly deposit you need to make is $1701.94.&lt;br&gt;
Thankfully, at this point we are finished with the ugly formulas and difficult calculations.  Everything from here on is simple arithmetic.&lt;br&gt;
c) How much did you deposit into you retirement account?&lt;br?
Answer: $1701.94 each month for 20 years, or 240 months: {{{1701.94*240 = 408465.60}}}&lt;br&gt;
You deposited a total of $408,465.60.&lt;br&gt;
d) How much did you receive in payments during retirement? &lt;br&gt;
Answer: $50,000 a year for 25 years = $1,250,000.&lt;br&gt;
e) How much of the money you received was interest? &lt;br&gt;
The difference between how much you took out and how much you put in: $1,250,000 - $408,465.60 = $843,534.40&lt;br&gt;&lt;br&gt;
Now follow the same steps to work the problem with your numbers.&lt;br&gt;
Be sure to enter the calculations correctly in your calculator, and verify that the numbers you get at each stage are reasonable.</PRE>